Hi welcome to the health care magic You are having viral and allergic upper respiratory tract infection.. (diagnosed by your physician) For your case i will recommend first investigate with CBC If you are having viral infection lymphocytosis can be seen and if having allergy then high eosinophils seen in CBC.... For viral inflammation decongestant and if wet cough then expectorant can be prescribed (as you have been prescribed) For allergic inflammation fexofenedine like drug better In week your symptoms will subside... No additional cough suppressant needed Take one tsp turmeric powder in hot milk daily Avoid excess spicy foods Drink warm water as having soothing effect If after inflammation over and dry cough not resolving or severe dry cough then only dextromethorphan like cough syrup can be prescribed Hope your concern solved Take care